Utilizând regula \( \left(a^{n}\right)^{m}=a^{n-m} \), scrieți sub forma unei singure puteri: \( \begin{array}{llll}\text { a }\left(5^{4}\right)^{6} ; & \mathrm{b}\left(7^{8}\right)^{3} ; & \mathrm{c}\left(23^{1}\right)^{17} ; & \mathrm{d}\left(13^{21}\right)^{7} \\ \mathrm{e}\left[\left(3^{2}\right)^{3}\right]^{4} ; & \mathrm{f}\left[\left(8^{5}\right)^{3}\right]^{6} ; & \mathrm{g}\left[\left(13^{5}\right)^{6}\right]^{4} ; & \mathrm{h}\left[\left(9^{2}\right)^{7}\right]^{12}\end{array} \)

Find the points of intersection for the system \[ \begin{array}{l}\mathrm{y} \geq 2 \mathrm{x}^{2}+3 \mathrm{x}-20 \\ \mathrm{y} \leq \mathrm{x}^{2}+\mathrm{x}-5\end{array} \]

MP) Use Structure A plumber charges a customer a one-time service fee of \( \$ 79, \$ 62 \) per hour for labor, and a surcharge of \( \$ 15 \) per hour due to the call being an emergency. Write an expression to represent the total charges for the plumber in two different ways.

Solve the system of quadratic inequalities: \[ \begin{array}{c}\mathrm{y}>\mathrm{x}^{2}-1 \\ \mathrm{y} \leq-\frac{1}{3} \mathrm{x}^{2}+5\end{array} \]

Solve the system of quadratic inequalities: \[ y>x^{2}-1 \]

The ratio of Ben's age to Ali's age is \( 3=2 \). Their total age is 140 years now What is Alils age?